The Laplace Transform and the Important Role it Plays

This revision fixes the following errors and suggestions that were found by my readers:

A few random typos and grammatical fixes:

Changed the imaginary variable symbol from 'i' to 'j' to be consistent across the book

This update continues the journey of understanding transfer functions. Section 2.6 is the only major addition to this revision. I struggled with this section (re-wrote it several times and I'm still not thrilled about the final product) so please write a ticket for any errors, confusions, or missing content so that I can improve this section over time.

This section covers the Laplace transform - one of the most important concepts in system analysis and theory. Rather then walk through how to perform the integral (I leave that for the math classes) this section walks through a way to understand the Laplace transform at an intuitive level. This is the final basic concept that is needed to fully understand transfer functions, which we'll close out in the next book release.

Thank you for all of your support and I hope this helps you on your quest to understand control theory on a more intuitive level. Cheers!

[fzigunov]

Hey, Brian, your explanation is perfect, that's exactly how I understand the Laplace transform. I wish I had somebody to explain things like this to me back when I was learning this, I had to figure it out the hard way!

Your work is really important and I will gladly recommend your channel to anyone that is struggling with controls!

Thanks for the effort and keep up with the good stuff!

[michaeljonez]

Okay. You win the prize! While personally certainly dependent on others as well (and a tad more clarification required), you have clearly detailed most of the remaining shrouded areas that not a single person on the Internet could do. Nice! Will purchase.

[ilxbox]

thank you so much for this explanation, my controls professor just kind of threw the laplace transform at us with no explanation of why we're using it instead of the fourier transform, or where the laplace transform comes from, etc. This is more informative.

[rogelioventura]

Your work is great. I really admire you and congratulate you for what you're doing. A quality product that is accesible to everyone. In name of every engineer I thank you!

[embronxer]

Thanks for the great work! Definitely getting the book.

[LongPham]

Thanks Brian! You made the hard subject really simple to understand.

[pardo]

i always thought this was the most difficult part of engineering it requires hundreds of hours of study and dedication and a huge load of previous knowledge.

[mnada]

Great work... I wish you put everything in your videos through your distinguished style in your book. It will be fantastic for sure.

[osmansafi]

thank alot for helping with the students.if any body have some problems in his/her lessons at any time you people are helping him/her alot indirectly so again thanks

[NXaiUL]

Awesome Video..
The thumbnail itself did it for me

[lironzilberberg]

I think the integral at 8:55 doesn't converge. you need to multiply the time domain function with the unit step function.

[stefnirk]

love your work :) keep it up. Going to check out what you added when I get home.

[williamscsharpwalkthroughs]

Great work- thanks a lot for this video, really helpful stuff

[unit]

Hi Brian Douglas, I found a typo. At 8:41 of this video, where it shows Page 79 of your book, the large text says "filling out the s plane produces a 3D surface with intersting peaks and valleys". The word "interesting" is misspelled. Good job on these videos, by the way, and thanks for making them!

[renatohugoviloriagonzalez]

Desde México, ahora si ya me quedó mas claro, tardé años para llegar a éste punto, soy cabeza lenta, pero se me clarifica better. Si siempre se me explicara así, no importa que sea en inglés.

[LawrenceKesteloot]

Is it accurate to say (at 1:00) that the frequency domain is two-dimensional? I think a two-dimensional function has two inputs (its domain has two dimensions). Here the domain is still one-dimensional (the frequency) and the *value* of the function (its range) has two components (magnitude and phase). I struggled with this a bunch because the Laplace transform's result is truly two dimensional in its domain (frequency and exponential) as well as its range (magnitude and phase, like the Fourier Transform). The jump from one- to two-dimensional domain (from FT to LT) is important, so I don't want readers to be confused by thinking that the FT's result is two-dimensional.

[kiddjmadd]

Great video! Possible typo for limits of integration on Laplace transform formula at 4:45. I thought it was from zero to infinity vs. minus infinity to infinity.

[hookwill]

Thank you so much! I FINALLY GET IT! This explained it so well thank you sir great work

[TheBdd]

Excellent presentation. I'm a self taught electronic engineer who is trying to learn to describe my designs mathematically.

[anasbiniftikhar]

Hi Brian,

Could you direct me to the link where you may have discussed Feed Forward control? Or could you post a new video lecture discussing feedforward?